Who's paying for the power to run the machine...

And no, the amount of money you put into mining does not exponentially increase your reward. That's the argument you're making. I mine just as many coins per watt as Riot does.

If you are paying for power, you are exchanging time/labor/energy for coins. That "money" IS your proof of work. You have 0$, you make a wallet and sell it for $50, you use that $50 to buy power and mine Bitcoin. There is no mining without you making the wallet. There is no power to be made without proof of work. The machine can't do any work at all if you don't provide it power. You can skip the economy and go straight to generating your own power, which just replaced the work making the wallet with the work to generate power directly instead of exchanging your time/labor/energy for it.